Depends what industry you are in, level of your profession, and audience that is going to read it. Paper based resume and internet based resumes can use different phrasing and length. Setting your profile on job boards is going to be different as well.
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I applied for a job and the deadline to apply was friday. I want to follow up with them this week

A. Should I wait until friday when it has been a week or is it ok to contact on Thursday?

B. Should I call them or email to say I wanted to check on the status of my application?
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